Preheat the oven to 350°F and line a baking sheet with parchment paper.
Whisk the flour, black cocoa powder, baking powder, and salt in a bowl.
In a separate bowl, beat the butter and granulated sugar until light. Add the egg and vanilla extract, then mix until combined.
Stir the dry ingredients into the wet mixture until a dough forms.
Roll the dough into 12 small balls and place them on the baking sheet. Flatten each slightly with your hand.
Bake for 10 to 12 minutes, then let the cookies cool completely on the sheet.
Mix the powdered sugar and milk in a bowl until smooth to make the white icing.
Place half the white icing in a piping bag. Add black food coloring to the remaining icing and place it in a second piping bag.
Flood each cookie with the white icing. Pipe thin black lines across the top, then drag a toothpick through the lines to form a web pattern. Let the icing set.